Civil Engineering Reference
In-Depth Information
L
b
a
1
a
22
a
1
Plate/Shell
Elements
Rigid
Elements
Equivalent
Frame
Figure 4.26
R e fi ned (
left
) and simplifi ed (
right
) fi nite element models for structural walls with openings
wall interface. Moreover, for walls with edge fl anges, additional vertical one-dimensional FEs, i.e. beam
elements, can be used at the interface between frame and the plate elements. These additional FEs resist
the axial loads associated with the global overturning moments while the plates are subjected primarily
to shear forces.
Several FE commercial programs do not allow connections between rigid diaphragms and walls
discretized with two-dimensional elements. In this case, the connection may be achieved by duplicating
the nodes of the wall located at each storey level. Slave nodes are connected to the master joint(s) of
the fl oor introduced in Section 4.5.3.3. Rigid links are used between slave nodes and the corresponding
nodes of the FEs on the wall. Alternatively, the nodes of plates or shells at the fl oor level are connected
by means of rigid rods to the nodes of the diaphragm. It is customary to assume that framed structures
are fully restrained against rotations at the base. For wall systems which possess large horizontal stiff-
ness, this assumption is, however, less accurate than in the case of slender columns. Refi ned assessment
requires including the different features of soil- foundation - structure interaction.
Problem 4.6
Defi ne a fi nite element model for the hybrid system shown in Figure 4.27. Comment on your
answer.
4.5.4 Masses
Both distributed and lumped mass representations are employed to model translational
m
t
and rotational
m
r
masses in earthquake response analysis. A mass matrix is a discrete representation of a continuous
mass distribution assembled for the purposes of FE analysis. Mass matrices representing distributed
